Bicuspid Aortic Valve and Exercise

I am a 42  year old female, 120 lbs (usually 112 - 115 lbs - unfortunately starting with the midlife weight gain), 5' 5", and normally heathy except for a congenital bicuspid aortic valve.  My last echo (2 years ago) showed that my stage 1 regurgitation has not changed.  I am due for another echo in a couple of months.  I had blood tests done in the last week and found out my thyroid function is perfect, but I am anemic and taking 3 - 300 mg of ferrogluc .

My exercise status is sedentary and I would like to start exercising, but I get palpitations from exercise.  I tried my daughter's eliptical trainer and only got 4 minutes into the easiest setting and my heart was racing and flopping all over the place.  I did not have any pain or faintness.  I have always been afraid to exercise due to palpitations, but really want to exercise for my health.  For years I noticed that walking up hills, or walking into the wind, etc. cause me to have a fast heart rate and palpitations.  I am so afraid to exercise.  I want to exercise for my health and to help lose a few pounds.  Friends of mine are using Tony Little's Gazelle and are losing a lot of weight. I would like to use it too, but....

Can I exercise safely?  Are the palpitations a sign that I shouldn't exercise or are a problem?

Are there tests to make sure the palpitations are not dangerous or cause any problems while exercising?

If I can exercise, what kinds should I do and how strenuous an exercise can I do?  Also, can I weight train?  I tried lifting weights but they too cause palpitations.